Republican Charlie Baker has narrowed the gap with Democratic Attorney General Martha Coakley in the Massachusetts governor’s race, signaling a potentially tight contest this fall, according to a new Boston Globe poll.

In series of hypothetical matchups, Baker trails Coakley by five percentage points, 32 to 37 percent and outpaces Treasurer Steven Grossman by six points, 32 to 26 percent. He also holds comfortable leads over the three other Democratic hopefuls, who remain essentially unknown to the electorate, the survey found. In all the matchups, two independent candidates, combined, pull from 9 to 11 percent support.

“We are now in a real horse race,” said pollster John Della Volpe, noting a series of other public polls in recent months have found Coakley, a Democrat, holding wider leads over Baker. “Now it’s within the margin of error.”

The first of more than 20 polls that the Globe plans to conduct of likely Massachusetts voters before Election Day 2014 found an electorate that believes the state is in better shape than the country as a whole but retains abiding concerns about the economy. That worry deeply colors the race to succeed Governor Deval Patrick, who is not running for a third term.

“Someone who will create jobs and is fiscally responsible are the dominant traits that voters look for in a governor,” Della Volpe said. “This is the prism through which voters will judge the candidates, at least at this juncture. Unless that changes, the landscape could favor Baker.”

Baker has promoted a political profile anchored by issues of fiscal responsibility, which poll respondents say is among the most important attributes they want to see in the next governor.

A major question, five months before voters choose a new governor, is the impact two wealthy, self-financing independent candidates will have on the general election. In key general election matchups, venture capital investor Jeffrey S. McCormick draws from 7 to 9 percent support. Lawyer and former business executive Evan Falchuk pulls a steady 2 percent.

Those results suggest that independent candidates are likely to a play significant role in the general election outcome, Della Volpe said. But he questioned the conventional wisdom that Baker, who must get a solid majority of unenrolled voters to win, would be hurt most by their presence on the ballot.

“Supporters of the two independent candidates do not seem to fit within a neat partisan framework,” he said. “McCormick voters today look like a Baker voter around fiscal responsibility while they look like Coakley voters when it comes to improving education.”

The survey, directed by Della Volpe’s firm, SocialSphere Inc., polled 602 likely Massachusetts voters from May 29 to June 3 on landlines and cellphones. Its margin of error is plus or minus 4 percent.

Fifty-five percent of those polled say things in the United States are on the wrong track, while only a quarter think they are headed in the right direction. Closer to home, sentiment is more evenly split: 40 percent believe the state is on the wrong path, while 44 percent say things are moving in right way in Massachusetts.

Asked to name the most important issue facing Massachusetts, about half cite ones related to the economy. Among the other issues volunteered: health care and government fiscal responsibility.

Respondents indicate economic issues are paramount as they mull what qualities matter to them in the next governor.

Eighty-five percent say a candidate’s ability to create jobs and improve the economy is very important as they choose whom to support for governor, while 82 percent say a candidate’s fiscal responsibility is very important. Seventy-six percent say a candidate’s commitment to improving education in public schools is very important.

None of eight other gubernatorial attributes the poll asked about — from a commitment to reducing economic inequality to not raising taxes to having private sector experience — get as strong a response.

Poll respondent Jason Ganz, a 22-year-old Democrat from Winchester who just graduated college, said in a follow-up interview he was undecided in the gubernatorial race. Issues such as job creation, support of small businesses, and taxes would likely influence how he ended up voting, he said.

“Obviously social issues are big, but I’m not that worried because it’s Massachusetts,” he said. “It will probably be economic type things that end up making my decision for me.”

Coakley is the best known of gubernatorial hopefuls: 56 percent have a favorable opinion of her, 36 percent have an unfavorable opinion of her, and a combined 7 percent either don’t recognize Coakley’s name or can’t say how they view her.

Forty-four percent have a favorable opinion of Baker, a former health insurance executive who lost to Patrick in 2010. Twenty percent have an unfavorable opinion of him, 15 percent recognize his name but can’t rate him, and 22 percent have not heard of him.

Almost 40 percent don’t recognize Grossman’s name, despite his being elected state treasurer in 2010. Thirty-five percent have a favorable opinion of him, while 11 percent have an unfavorable opinion of him, and 15 percent recognize his name but can’t rate him.

But Della Volpe said the numbers indicate that if Grossman were to win the Democratic nomination, it could still be a tight race in the fall.

The Globe will release a poll next Friday that examines potential Democratic primary matchups.

This week’s poll found that the three other Democrats — former homeland security official Juliette Kayyem, biopharmaceutical executive Joseph Avellone, and former Medicare and Medicaid chief Donald M. Berwick — are still struggling to gain public recognition. Respectively, 77, 78, and 83 percent don’t recognize their names.

There is also a contested primary election on the Republican side. Baker is being challenged for the GOP nomination by businessman Mark R. Fisher. But the poll found more than three-quarters of likely voters do not know Fisher, who affiliates himself with the Tea Party movement. In an interesting twist, 14 percent of likely Massachusetts voters polled say they consider themselves supporters of the Tea Party movement.

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